What is the solution for y^{''}+5y^'+6y=2e^x ?

The solution for y^{''}+5y^'+6y=2e^x is y=c_{1}e^{-2x}+c_{2}e^{-3x}+1/6 e^x

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y^{''}+5y^'+6y=2e^x

y^{^{''}} + 5 y^{^{'}} + 6 y = 2 e^{x}

y = c_{1} e^{- 2 x} + c_{2} e^{- 3 x} + \frac{1}{6} e^{x}

Solution steps

y^{''} (x) + 5 y^{'} (x) + 6 y = 2 e^{x}

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} e^{- 3 x} + \frac{1}{6} e^{x}

y = c_{1} e^{- 2 x} + c_{2} e^{- 3 x} + \frac{1}{6} e^{x}

\frac{d}{d x} (in (sec (x)))

n = 1 \sum \infty \frac{2}{e ^{n - 3}}

y^{^{''}} - \frac{2}{x} y^{^{'}} - \frac{4}{x ^{2}} y = 3 x^{2}

x \to 1 + lim (x^{3} - 4)

x \to - 1 lim (\frac{2 x}{x + 1})

What is the solution for y^{''}+5y^'+6y=2e^x ?
The solution for y^{''}+5y^'+6y=2e^x is y=c_{1}e^{-2x}+c_{2}e^{-3x}+1/6 e^x